Integrated circuit (IC) design on a chip, e.g., LSI Logic Corporation's RapidSlice™, and the like, usually contains physical memories with fixed capacities and fixed data widths. However, a customer's IC design may contain logic memories with different capacities and data widths. Conventionally, mapping customer's logic memories to given physical memories is done manually, which is a very tedious and time-consuming process. Therefore, it would be advantageous to provide a controller for automatically mapping a customer's arbitrary logic memory into physical memories on a chip.